Prince William visits pregnant Kate at the hospital

Prince William reportedly spent about six hours with his pregnant wife Kate on Tuesday at King Edward VII Hospital, where the duchess of Cambridge is being treated for acute morning sickness.

He did not speak to the assembled media mob coming or going, but was said to have left with a smile on his face.

Also visiting Kate in the afternoon were the royal gynecologist, Dr. Alan Farthing, and her primary OB/GYN, Dr. Marcus Setchell, the BBC reported. Tell us you don't love the idea of a royal gynecologist, eh?

Don't expect the queen to make an appearance, however.

"She doesn't normally go because it disrupts the running of the hospital," a palace source told People. "And the duchess just wants to recover and get out."

One scientific note that has tongues wagging: Hyperemesis gravidarum, or HG, is relatively rare overall but can be caused when a woman is carrying twins or other multiples, according to Booster Shots, which has lots more information on the condition.

No due date has been announced, though Kate is believed to be in her first trimester of pregnancy. HG usually hits when a woman is four to six weeks along and resolves in most cases by the 20th week, according to Booster Shots. If hospitalized, a woman might spend two or three days being treated for HG.

Beyond the hospital, speculation was hopping with bookmakers about the baby's gender and possible name, with money leaning toward a girl with a traditional family moniker, perhaps Elizabeth, Mary, Frances or Victoria. Diana was also in the running, though at longer odds. Boy names included John and Charles.